Question
Assume that giraffes have a mean height of 16.0 feet and a standard deviation of 2.1 feet. Two giraffes are selected from a nature preserve with heights of 13.1 feet and 20.3 feet respectively. Determine the z-scores associated with each giraffe. Would either of those giraffes be considered significantly short or significantly tall? Why or why not?
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Answer to a math question Assume that giraffes have a mean height of 16.0 feet and a standard deviation of 2.1 feet. Two giraffes are selected from a nature preserve with heights of 13.1 feet and 20.3 feet respectively. Determine the z-scores associated with each giraffe. Would either of those giraffes be considered significantly short or significantly tall? Why or why not?
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Solution:
Z score is given by
z=\frac{\overline{x}-\mu}{\sigma}
For shorter giraffe,
z=\frac{13.1-16}{2.1}
z\approx-1.38
For taller giraffe,
z=\frac{20.3-16}{2.1}
z\approx2.05
Both z scores are between z=-3 and z=3. Therefore, neither are significantly short or tall.
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